isogeny
|aɪ-sə-dʒə-ni|
/ˈaɪsədʒəni/
same-kind finite-kernel map
Etymology
'isogeny' originates from Greek, specifically the elements 'isos' and 'genos', where 'isos' meant 'equal' and 'genos' meant 'birth, kind, race'.
'isogeny' entered scientific usage via New Latin/French (e.g. New Latin 'isogenia' or French 'isogénie') and was adopted into English in mathematical contexts in the late 19th to early 20th century.
Initially formed from roots meaning 'equal origin' or 'same kind'; over time it became a technical mathematical term denoting a specific type of finite-kernel surjective morphism between algebraic groups (especially elliptic curves and abelian varieties).
Meanings by Part of Speech
Noun 1
in algebraic geometry and number theory, an isogeny is a nonzero morphism (group homomorphism) between algebraic groups such as elliptic curves or abelian varieties that is surjective with finite kernel (equivalently, a finite-degree surjective homomorphism).
Two elliptic curves E1 and E2 are isogenous if there exists a nonzero isogeny φ: E1 → E2.
Synonyms
Last updated: 2025/12/07 05:42